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Theorem bnj1071 33646
Description: Technical lemma for bnj69 33679. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1071.7 𝐷 = (ω ∖ {∅})
Assertion
Ref Expression
bnj1071 (𝑛𝐷 → E Fr 𝑛)

Proof of Theorem bnj1071
StepHypRef Expression
1 bnj1071.7 . . 3 𝐷 = (ω ∖ {∅})
21bnj923 33437 . 2 (𝑛𝐷𝑛 ∈ ω)
3 nnord 7811 . 2 (𝑛 ∈ ω → Ord 𝑛)
4 ordfr 6333 . 2 (Ord 𝑛 → E Fr 𝑛)
52, 3, 43syl 18 1 (𝑛𝐷 → E Fr 𝑛)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1542  wcel 2107  cdif 3908  c0 4283  {csn 4587   E cep 5537   Fr wfr 5586  Ord word 6317  ωcom 7803
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-ral 3062  df-rab 3407  df-v 3446  df-dif 3914  df-in 3918  df-ss 3928  df-uni 4867  df-tr 5224  df-po 5546  df-so 5547  df-fr 5589  df-we 5591  df-ord 6321  df-on 6322  df-om 7804
This theorem is referenced by:  bnj1030  33656  bnj1133  33658
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